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Give three equivalent properties of conservative vector fields. Consider the vector field F defined on an open connected region R in R² (or D in R³). Select all that apply. A. There exists a potential function such that p = VF. F. dr = 0 on all simple smooth closed oriented curves C in R. B. c. F. dr = 0 on all simple smooth open oriented curves C in R. p(A)-p(B) for all points A and B in R and all smooth oriented curves C from A to B. (A)- □D. F. dr = E. There exists a potential function

Give three equivalent properties of conservative vector fields. Consider the vector field F defined on an open connected region R in R² (or D in R³). Select all that apply. A. There exists a potential function such that p = VF. F. dr = 0 on all simple smooth closed oriented curves C in R. B. c. F. dr = 0 on all simple smooth open oriented curves C in R. p(A)-p(B) for all points A and B in R and all smooth oriented curves C from A to B. (A)- □D. F. dr = E. There exists a potential function

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Give three equivalent properties of conservative vector fields. Consider the vector field F defined on an open connected region R in R² (or D in R³). Select all that apply. A. There exists a potential function such that p = VF. ☐B. F. dr = 0 on all simple smooth closed oriented curves C in R. c. fF.dr=00 r=0 on all simple smooth open oriented curves C in R. □D. F.dr = (A) - (B) for all points A and B in R and all smooth oriented curves C from A to B. ☐E. There exists a potential function such that F = V. OF. fF.dr= =drp(B) - p(A) for all points A and B in R and all smooth oriented curves C from A to B.
Transcribed Image Text:Give three equivalent properties of conservative vector fields. Consider the vector field F defined on an open connected region R in R² (or D in R³). Select all that apply. A. There exists a potential function such that p = VF. ☐B. F. dr = 0 on all simple smooth closed oriented curves C in R. c. fF.dr=00 r=0 on all simple smooth open oriented curves C in R. □D. F.dr = (A) - (B) for all points A and B in R and all smooth oriented curves C from A to B. ☐E. There exists a potential function such that F = V. OF. fF.dr= =drp(B) - p(A) for all points A and B in R and all smooth oriented curves C from A to B.
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